Method and System for Tank Refilling

ABSTRACT

Disclosed is an improved analytical method that can be utilized by hydrogen filling stations for directly and accurately calculating the end-of-fill temperature in a hydrogen tank that, in turn, allows for improvements in the fill quantity while tending to reduce refueling time. The calculations involve calculation of a composite heat capacity value, MC, from a set of thermodynamic parameters drawn from both the tank system receiving the gas and the station supplying the gas. These thermodynamic parameters are utilized in a series of simple analytical equations to define a multi-step process by which target fill times, final temperatures and final pressures can be determined. The parameters can be communicated to the station directly from the vehicle or retrieved from a database accessible by the station. Because the method is based on direct measurements of actual thermodynamic conditions and quantified thermodynamic behavior, significantly improved tank filling results can be achieved.

PRIORITY STATEMENT

This application is a continuation-in-part of U.S. patent applicationSer. No. 12/982,966, filed Dec. 31, 2010, the contents of which areincorporated by reference, in their entirety, which claims prioritypursuant to 35 U.S.C. §119(e) from U.S. Provisional Patent ApplicationNos. 61/326,375 and 61/332,919, the contents of which are alsoincorporated by reference, in their entirety.

BACKGROUND OF THE INVENTION

The safety and convenience of hydrogen tank refueling are recognized asimportant considerations in determining the ultimate success of hydrogenfueled vehicles in the marketplace. Under current safety guidelines, therefueling of compressed hydrogen tanks are to be conducted in a mannerthat prevents the tank from overheating (temperatures exceeding 85° C.)during refueling and/or from overfilling the tank to a point at whichthe pressure could exceed 125% of normal working pressure (NWP) at anytime. Because of the number of unknown parameters associated withconventional hydrogen tank refueling procedures, the refuelingoperations tend to be somewhat conservative, thereby trading performanceand efficiency, particularly with respect to end of fill density (SOC %)and/or unnecessary levels of pre-cooling, for an increased safetymargin. A SOC of 100%, for example, corresponds to a tank at NWP and 15°C.

This tradeoff is especially significant in non-communication fuelingoperations in which the parametric assumptions are even moreconservative. Because the hydrogen fueling station does not haveinformation about the tank that it is filling, very conservativeassumptions are used to encompass a wide range of possible tankconfigurations and initial tank conditions and provide filling solutionsthat will not exceed the system safety limits. In SAE TIR J2601, thedisclosure of which is incorporated herein by reference, in itsentirety, these conservative assumptions are incorporated into a seriesof lookup tables for hydrogen tank filling. Working from parametersincluding the tank volume, starting pressure, ambient temperature andstation pre-cooling set point, the lookup tables are then used fordetermining a pressure ramp rate and final target pressure. Whileapplication of these lookup tables tends to provide for safe refillingunder virtually all conditions and for virtually all tank systems, giventhe conservative nature of the associated assumptions, the resultinghydrogen tank filling operation may take longer, achieve lower finalfill pressures and/or require lower hydrogen station pre-coolingtemperatures than necessary to fill a particular tank system.

An additional limitation of the refilling procedures defined by SAE TIRJ2601 is the lack of any method or procedure for a hydrogen tank fillingstation to compensate or adjust for situations in which its actualoperating conditions fall outside of the allowed tolerances. Forexample, if the pre-cooling temperature is above the design set point asthe result of multiple consecutive refills, the lookup tables defined inSAE TIR J2601 cannot be used. Efforts to avoid this out of specificationcondition can lead to an overdesigned hydrogen tank filling station(excessive cooling for ensuring that the pre-cooling target temperatureis maintained), thereby driving up station cost.

Conversely, failing to ensure that the pre-cooling target temperature ismaintained can inconvenience customers by preventing them from refillingtheir tanks in a timely manner (as a result of the delay(s) incurredwhile waiting for the pre-cooling temperature to come intospecification), thereby tending to reduce customer satisfaction, stationrevenue and/or repeat business. Further, operating a hydrogen fuelingstation with a constant pre-cooling temperature regardless of currentambient conditions increases the energy usage and reduces well-to-wheelenergy efficiency. In order to reduce energy use, a hydrogen tankfilling station should be operated at the highest possible pre-coolingtemperature that strikes a balance between customer-acceptable refuelingtimes and satisfactory safety margins for the refueling operation.

BRIEF SUMMARY

The improved MC Method as detailed infra provides a new tank fillingmodel based on the total heat capacity of the hydrogen fueling systemand an advanced algorithm based on that model for improving theperformance of hydrogen filling stations under a broad range ofoperating conditions and, in particular, includes additionalconsideration of heat transfer to the hydrogen from downstreamcomponents. This modified algorithm, as applied stepwise in the MCMethod, can be used to enhance fueling performance relative to thatavailable under SAE TIR J2601 by utilizing additional thermodynamicinformation about the tank and filling systems. The MC Method may beapplied to virtually any combination of tank system Normal WorkingPressure (NWP) and any compressed hydrogen tank system. The additionalconsideration of heat transfer to the hydrogen can permit fuelingoperations under conditions outside of current SAE TIR J2601 tables,thereby tending to improve both fill speed and fill quality (SOC %),while reducing the costs incurred by the hydrogen stations in effectingsuch operations.

BRIEF DESCRIPTION OF THE DRAWINGS

Example embodiments described below will be more clearly understood whenthe detailed description is considered in conjunction with theaccompanying drawings, in which:

FIG. 1 illustrates the modeling of a hydrogen storage tank duringrefueling as an open system with an unsteady flow control volume model.For the purpose of this disclosure, the control volume is defined as theboundary between the gas and the liner with heat being transferredthrough the boundary of the control volume and into the liner of thetank.

FIG. 2 illustrates a temperature v. time curve for a hydrogen tankrefueling procedure, reflecting use of the adiabatic temperature incalculating the heat transfer with the heat transferred from thehydrogen being described by Equation [5] infra.

FIG. 3 illustrates a constant heat flux model showing temperaturedistribution dependent on time with adiabatic boundary condition with aconservative assumption of no heat transfer from the outside of the tankso that the actual final temperature in the tank is expected to beslightly lower than the value calculated in light of this assumption.

FIG. 4 illustrates a temperature distribution of a section of acomposite tank immediately after a vehicle refueling.

FIG. 5 illustrates a simplified representation of a hydrogen tank havingan imaginary characteristic volume of combined mass and specific heatcapacity MC, with adiabatic external boundary.

FIG. 6 illustrates a typical vehicle fill in 3 minutes with a Type 3tank that produces an end-of-fill MC value of 62 that then tends toincrease as the tank cools. This trend of MC v. time is characteristicfor a given tank system, and can be used in predicting the temperatureresult of longer vehicle fueling times.

FIG. 7 illustrates MC v. fill time for a “default” SAE TIR J2601-70 MPaType 4 tank. This graph is derived from the Type B (7-10 kg) 70 MPastation tables of SAE TIR J2601.

FIG. 8 illustrates a potential Test Matrix for tank characterization

FIGS. 9A and 9B illustrate MC v. U_(adiabatic)/U_(init) for 3 minutefills and 30 second approximations of a Type 3 tank from which thecoefficients A and C can be determined.

FIG. 10 illustrates ΔMC v. time for fill times having a duration of morethan 3 minutes from which the coefficients g, k, and j can be determinedfor describing the behavior of MC for fill times in excess of 3 minutes.

FIG. 11 illustrates a comparison of the hydrogen station operatingenvelopes to the existing refueling standards, showing several gaps inthe coverage of existing or anticipated operating regimes.

FIG. 12 illustrates information required for fully utilizing the MCMethod for determining a fueling protocol under a given set ofconditions.

FIG. 13 illustrates the MC Method first step—determining the fuelingtime based on a higher than ambient temperature, i.e., hot soak (HS),condition in which T_(init) can be represented by T_(HSinit) forconvenience.

FIG. 14 illustrates the MC Method second step—determining the pressuretarget based on using a colder than ambient, i.e., cold soak (CS),condition in which T_(init) can be represented by T_(HSinit) forconvenience.

FIG. 15 illustrates the MC Method third step, using the pressure targetfrom the second step in determining the expected result and, if inexcess of the target pressure, reducing the target density andrecalculating in an iterative manner to match the pressure target at thefinal temperature.

FIG. 16 illustrates the results obtained from a 35 MPa Type 3 Tank Fillunder a 35° C. ambient with 5° C. Pre-cooled Hydrogen and 5 MPa StartPressure. T_(final) target is 69.2° C., bounded by Hot Soak at 74.3° C.and Cold Soak at 62.3° C.

FIG. 17 illustrates Result of 50 MPa Type 4 Tank Fill from 30° C.Ambient with −15° C. Pre-cooled Hydrogen and 2 MPa Start Pressure.T_(final) target is 86.7° C., bounded by Hot Soak at 89.0° C. and ColdSoak at 83.0° C. Note that the target pre-cooling temperature was −20°C., which verified the difficulty in practice of keeping a specifiedpre-cooling temperature.

FIG. 18 illustrates 70 MPa Type 4 Tank Test from 25° C. Ambient at 17MPa Start Pressure with −7.5° C. Pre-cooling. T_(final) target is 76.6°C., bounded by Hot Soak at 81.0° C. and Cold Soak at 70.0° C.

FIGS. 19A and 19B illustrate Calculation of the Constants of the MCEquation (Equation [13]) for the Type 3 Tank and show that the datagenerated during verification filling under different conditionscompliments the data that was used to generate the constants originally.The model is robust to different conditions.

FIG. 20 illustrates Error between T_(final) as calculated by the MCMethod and the actual measured final temperature at the end of the fill.

FIGS. 21A and 21B illustrate Sensitivity Analysis of Type 3 and Type 4Tanks, respectively, to Input Errors Using the MC Method.

FIG. 22 illustrates a comparison of fueling methods showing the impactof adding the MC Method to existing fueling protocols.

FIG. 23 illustrates a relationship between nozzle temperature deviationfrom pre-cooling temperature, flow rate, pre-cooling temperature, andambient temperature measured during fill testing. This relationship is,of course, dependent on the specific implementation of components for agiven fueling station or test stand.

FIG. 24 illustrates equations of a curve fit to the NIST HydrogenProperty Database for hydrogen gas utilized for determining internalenergy (given temperature and pressure), enthalpy (given temperature andpressure), temperature (given internal energy and pressure), and density(given temperature and pressure) of hydrogen gas.

FIG. 25 illustrates a fueling system 2500 in which additional componentsare arranged between the point 2508 at which the temperature andpressure of the hydrogen leaving the dispenser body is measured and thepoint at which the hydrogen enters the tank 2512.

It should be noted that these Figures are intended to illustrate thegeneral characteristics of methods, structure and/or materials utilizedin the example embodiments and to supplement the written descriptionprovided below. These drawings are not, however, to scale and may notprecisely reflect the precise structural or performance characteristicsof any given embodiment, and should not be interpreted as defining orlimiting the range of values or properties encompassed by exampleembodiments.

DETAILED DESCRIPTION

The goal of the methods and systems detailed in this disclosure is toprovide an improved hydrogen filling model and system utilizing anappropriate algorithm that can be utilized in any gas tank fillingoperation for improving the accuracy in predicting the end-of-filltemperature and pressure conditions for a range of hydrogen tanks acrossa wide range of operating conditions. Implementation of the methods andsystems detailed below during hydrogen tank refueling events can improvethe efficiency, accuracy and/or safety of the refueling operation byreducing the chance of overfilling and/or overheating a hydrogen tank.

Accurately estimating the end-of-fill temperature achieved by arefueling operation can be difficult, which is why communicationrefueling has been developed. Such systems rely on temperature andpressure information that is transmitted directly to the hydrogen tankfilling station through one or more communication device(s) including,for example, the Infrared Data Association (IRDA) interface detailed inSAE TIR J2799, the disclosure of which is incorporated herein byreference, in its entirety. It is the absence of this temperature andpressure data requires non-communication fueling protocols toincorporate a relatively large margin of safety, particularly in thoseinstances involving other unknown parameters including, for example, thetank type, the tank size, the aspect ratio, the number of tanks and/orthe hot or cold soak status.

Although full-communication fueling can be used to provide the tankparametric data to the hydrogen tank filling station,full-communications fueling adds more cost and complexity to both thestation and the vehicle and tends to raise additional concerns,particularly with regard to the use of in-tank sensors. Accordingly,there remains a need for a method for providing sufficiently accuratepredictions regarding the temperature and/or pressure of the hydrogen inthe tank over the course of a refueling operation without requiringfull-communication protocols and hardware.

In order to provide an accurate prediction of the temperature of thegas, both the amount of energy that has been transferred to the tank andthe quantity of heat that has been transferred from the gas to the wallof the tank are estimated. Many studies have been conducted in trying tounderstand and quantify the end-of-fill temperature.

By modeling a hydrogen tank as an open system in unsteady flow, asillustrated in FIG. 1, it is possible to estimate the amount of energythat has been transferred to a tank by measuring the enthalpy of theincoming hydrogen stream and monitoring the temperature of the tank. Forthe purposes of this disclosure, the control volume is defined as theboundary between the gas and the tank liner with heat being transferredthrough the boundary of the control volume and into the liner of thetank. The total heat transfer in and out of the system, Q, is reflectedin Equations [1] and [2].

$\begin{matrix}{{{Q - W} = {{\int_{m_{e}}{h_{e}\ {m}}} - {\int_{m_{i}}{h_{i}\ {m}}} + {\Delta \; E_{system}}}},{{{and}\mspace{14mu} {setting}\mspace{14mu} m_{e}} = {{0\mspace{14mu} {and}\mspace{14mu} W} = 0}}} & \lbrack 1\rbrack \\{Q = {{- {\int_{m_{i}}{h_{i}\ {m}}}} + ( {{m_{2}u_{2}} - {m_{1}u_{1}}} )_{cv}}} & \lbrack 2\rbrack\end{matrix}$

-   -   where    -   Q=Total heat transfer in and out of the system        (kJ)_((Heat transfer out of the system is negative by convention))    -   W=work done to the system (kJ)    -   m_(e)=mass exiting the system (kg)    -   h_(e)=enthalpy of the fluid exiting the system (kJ/kg)    -   m_(i)=mass entering the system (kg)    -   h_(i)=enthalpy of the fluid entering the system (kJ/kg)    -   m₁=mass of the fluid in the control volume at the initial state        (kg)    -   m₂=mass of the fluid in the control volume at the final state        (kg)    -   u₁=internal energy of the fluid in the control volume at the        final state (kJ/kg)    -   u₂=internal energy of the fluid in the control volume at the        initial state (kJ/kg)    -   cv designates the state of the control volume.

The enthalpy can be determined by measuring the temperature and pressureof the hydrogen in the flow stream, preferably at a point close to or atthe tank inlet, with the mass flow into the tank being measured orcalculated from initial and final conditions. In some instances,however, the temperature and pressure of the hydrogen in the flow streamcan be measured well upstream of the tank inlet as illustrated in FIG.25. To estimate the final temperature of the gas during or after arefueling procedure, the actual heat transfer, Q, from the gas into thetank wall needs to be estimated. Because Equation [2] only givesinformation for the internal energy state of the tank, a tool, such asthe National Institute of Standards and Technology (NIST) ThermophysicalProperty Database, is used to look up the temperature from the internalenergy properties of the target gas, e.g., hydrogen. A curve fit to theNIST data used here for internal energy is illustrated in FIG. 2. Thedifference between the adiabatic internal energy and the measuredinternal energy (u₂ at measured temp and pressure) is the quantity ofheat that is transferred from the control volume, and can be determinedfrom test data.

$\begin{matrix}{u_{adiabatic} = \frac{{m_{i}u_{i}} + {\int_{m_{i}}{h_{i}\ {m}}}}{m_{2}}} & \lbrack 3\rbrack \\{m_{2} = {{m_{1} + {\int_{m_{i}}\ {m}}} = {m_{1} + m_{i}}}} & \lbrack 4\rbrack \\\begin{matrix}{Q = {m_{2}( {u_{adiabatic} - u_{2}} )}} \\{= {m_{cv}( {u_{adiabatic} - u_{2}} )}} \\{= {m_{cv}{C_{v}( {T_{adiabatic} - T_{final}} )}}}\end{matrix} & \lbrack 5\rbrack\end{matrix}$

-   -   where    -   u_(adiabatic)=adiabatic internal energy—if there was no heat        transferred from the system (kJ/kg)    -   m₂=m_(cv)=end-of-fill mass of hydrogen in the control volume        (kg)    -   T_(adiabatic)=adiabatic temperature—if there was no heat        transfer from the system (K)    -   T_(final) hydrogen temperature at the end of the fill (K)    -   C_(v)=Specific heat capacity of hydrogen at constant volume        (kJ/kgK)

FIG. 2 illustrates a Temperature v. Time curve for a hydrogen tankrefueling procedure in which the adiabatic temperature, T_(adiabatic),is used in calculating the heat transfer. The heat transferred from thehydrogen can be described by Equation [5] as detailed above. Thisprovides a tool for analyzing actual test data to determine the amountof heat that has been transferred from the hydrogen gas out of thecontrol volume, or into the structure of the tank. Note that theadiabatic internal energy is based only on initial conditions of thetank (initial mass of hydrogen and initial temperature) and theconditions of the hydrogen delivered from the station (enthalpy and fillmass). There is no dimension of time in the adiabatic condition, and soit is an appropriate reference for results for all time periods. If areliable method to predict the heat transfer can be found, then itshould be possible to directly calculate the final state of the hydrogenin the tank.

To calculate the end-of-fill gas temperature (T_(final)) is necessary toestimate the amount of heat that is absorbed by the tank wall. Onemethod of calculating the total heat transfer is to integrate thetemperature distribution over the tank volume at the end of a vehiclerefueling procedure. In 2003, General Dynamics conducted a series oftests aimed at understanding the relationship between final tanktemperature and filling time with the results being reported in Eihusen,J. A., “Application of Plastic-Lined Composite Pressure Vessels ForHydrogen Storage,” World Hydrogen Energy Conference, 2004 (Eihusen), thedisclosure of which is incorporated herein by reference, in itsentirety. As detailed in Eihusen, a series of filling tests wereconducted while measuring the temperature of the gas and of variouslocations in the hydrogen tank wall.

These results indicated that during a refueling operation, the heattransfer process was one in which the temperature of the outer surfaceof the tank did not rise, indicating that no appreciable quantity ofheat was being transferred through the tank wall. Based on theseresults, General Dynamics proposed a heat transfer model for predictingthe temperature distribution within the tank wall which was based on aGreen's Function solution to the general heat equation with a constantheat flux on the inside surface and an adiabatic boundary on the outsidesurface. See Equation [6]. A constant heat flux model showingtemperature distribution dependent on time with an adiabatic boundarycondition is illustrated in FIG. 4. Note that the assumption of no heattransfer from the outside of the tank is conservative, meaning that theactual final temperature in the tank can tend to be somewhat lower thanthe final temperature calculated using this assumption.

${T( {x,t} )} = {{\frac{q_{0}L}{k}\{ {\frac{\alpha \; t}{L^{2}} + {\frac{1}{2}( \frac{x}{L} )^{2}} - \frac{x}{L} + \frac{1}{3} - {\frac{2}{\pi^{2}}{\sum\limits_{m = 1}^{100}{{\frac{1}{m^{2}}\lbrack {\cos ( {m\; \pi \frac{x}{L}} )} \rbrack}^{{- m^{2}}\pi^{2}\frac{\alpha \; t}{L^{2}}}}}}} \}} + T_{0}}$

-   -   where    -   T(x,t)=Temperature at liner depth=x, time=t    -   q₀=Normalized heat flux of the liner (determined from testing)    -   L=Thickness of the liner    -   k=Thermal conductivity of the liner    -   α=Thermal diffusivity of the liner    -   T₀=Initial temperature of the liner

Inherent in this approach is the assumption that given an initial set ofconditions (hydrogen tank temperature, fuel gas temperature andpressure) the fueling temperature result and the temperaturedistribution result is purely dependent on time. The amount of heattransferred to the liner during a refueling procedure could be estimatedby integrating the temperature distribution over the volume of theliner. General Dynamics found that for the given set of tests, thismodel predicted the final tank temperature within 3K. The assumption ofa constant heat flux (or of temperature dependence only on time) is,however, both interesting and problematic. Different initial conditions(temperature of the tank, initial fill mass of the tank, temperatureand/or pressure of the incoming gas) can produce different temperaturegradients, and hence a different average heat flux. Further, the heatflux would depend on the conditions of the boundary layer between thegas and the wall—a change in the velocity, density, or temperature ofgas flow over the wall resulting from forced and/or free convectioninside the tank would result in a corresponding change in the heattransfer. As these conditions do tend to vary during the actual tankfilling procedure, the heat flux can also tend to vary over the courseof the filling procedure.

Furthermore, hydrogen refueling tests by the Japan Automobile ResearchInstitute (JARI) as reported in Hirotani, R., et al., JARI, “ThermalBehavior in Hydrogen Storage Tank for Fuel Cell Vehicle on FastFilling,” World Hydrogen Energy Conference, 2006, the disclosure ofwhich is incorporated herein by reference, in its entirety, revealed asignificant temperature distribution within the gas itself, up to a 30Kdifference throughout the tank, which would influence the heat flux. Thepresence of such temperature distributions further complicates theanalysis of data as well because it renders it difficult, if notimpossible, to know precisely how accurately a particular temperaturemeasurement taken inside the tank represents the bulk properties of thetank.

Relative to the bulk temperature, if the thermocouple is measuring atemperature that is warmer or cooler than the average bulk temperature,the calculated values can obviously be less accurate. Although it iscustomary to assume that temperature measurements taken at or near thecenterline of the tank can represent the average (bulk) gas temperature,the magnitude of the error(s) associated with this assumption areunknown in practice. Data taken during the development of the MC formulafueling control method and system disclosed in U.S. patent applicationSer. No. 12/982,966 showed unexplained errors of ±5K between thethermocouple output and the expected bulk gas temperature. Modelingefforts by the SAE TIR J2601 committee similarly reflected errors of upto 9K between the modeled temperature and the measured data despite theuse of thermocouples that have an accuracy of approximately ±1K. Thesereal world complications to the temperature gradient modeling make itdifficult in practice to apply a heat transfer model for directlyestimating the temperature distribution in order to calculate theend-of-fill temperature (with reliance on one or more temperaturesignal(s) during communication fueling operations introducing a degreeof uncertainty).

Additional adjustments to the heat mass adjustments may be made tocompensate for heat gained from or lost to the structures and componentsarranged between a dispenser and a tank as illustrated in FIG. 25. Theheat transfer to the H₂ may be represented with a modified equation forthe value of u_(adiabatic) in such systems as illustrated by Equation[7] below:

Q _(connector) =C _(dispenser)(T _(gas(initial)) −T _(gas))+C_(vehicle)(T _(ambient) −T _(gas))  [7]

Wherein C_(dispenser) is the heat capacity (Joules/K) of thecomponent(s) associated with the dispenser, T_(gas(initial)) is theinitial gas temperature (before any H₂ flow has occurred) measured atpoint 2508, C_(vehicle) is the heat capacity of the component(s)associated with the vehicle and T_(gas) is the gas temperature measuredat the same point during the filling operation. Q_(connector) representsthe heat added to the gas during fueling by the components that comprisethe fluidic connection between the dispenser 2506 and the tank 2512.This adjustment alters the u_(adiabatic) equation accordingly:

$\begin{matrix}{u_{adiabatic} = \frac{U_{initial} + {m_{add}h_{average}} + Q_{connector}}{m_{cv}}} & \lbrack 8\rbrack\end{matrix}$

for calculating the specific adiabatic internal energy.

Q_(connector) can be calculated continuously or periodically during thefill operation based on measured gas temperature T_(gas) as the gasleaves the dispenser body. It is anticipated that T_(gas) can varyduring the fill operation and that the heat adjustment Q_(connector) canvary accordingly over the course of the fill operation. The use of theQ_(connector) adjustment represents a conservative approach in that itassumes that all of the components arranged between the dispenser bodyand the tank can achieve T_(gas) during the course of the fill operationwhen, in fact, they can tend to be warmer than the gas throughout therelatively brief duration of the fill operation that can be achievedwith the improved MC Method. As with the tank calculations, it isassumed that the construction and configuration of the relevantcomponents is such that heat transfer from the ambient to the H₂ throughthe components can be minimal and, consequently, can be ignored for thepurposes of these calculations.

This modified MC Method does, however, automatically adjust for thecurrent condition of the fueling station. For example, if the fuelingstation had recently completed another fill operation, thenT_(gas(initial)) may be significantly colder than T_(ambient). Thiscondition tends to result in a substantially linear response between astation with a hot condition and a station cold condition. The lookuptables provided in J2601 are not, however, constructed in such a way asto adjust for such a situation as they are drawn only to hot or coldconditions and do not provide sufficient guidance for intervening, andpossibly more common, conditions.

While complex heat transfer models and analysis have been used in thepast to explain the results of tank filling tests, the approachdescribed herein utilizes a simplified heat capacity model, thedevelopment of which is described in more detail below and furtherillustrated in the associated figures. Application of other methods,results and testing has confirmed the utility and applicability of thissolution for predicting the heat transfer characteristics of the systemwith sufficient accuracy.

Consider a tank that has just completed a vehicle refueling in a shortperiod of time. As illustrated in FIG. 5, the inside of the tank is muchhotter than the outside of the tank, due to the conversion of pressureenergy to sensible energy of the high pressure hydrogen that was justrecently injected into the tank. Calculating the actual temperaturedistribution is difficult because 1) there is a temperature distributionbetween the hydrogen in the tank and the liner due to boundaryconditions, 2) there is a temperature distribution through the liner,contact resistances between layers, 3) there is a temperaturedistribution through the various layers of the tank and 4) there is atemperature distribution between the outside of the tank and theenvironment due to the outer boundary conditions. And as discussedpreviously, there may also be a temperature distribution within thehydrogen in the tank itself on the order of 30K. Each layer has adifferent specific heat capacity that might also be dependent ontemperature, and each layer is composed of a different mass. Given allof these complexities, it is exceedingly difficult, if not impossible,to calculate the precise temperature distributions through the wall ofthe tank.

The biggest difficulty in considering a heat transfer model based on aprecise calculation of the temperature distribution in the wall of ahydrogen tank is that it requires a solution to the temperaturedistribution for the entire time domain of a refueling event, a solutionwhich is difficult to achieve in practice. Accordingly, the methodutilizes a combined mass and specific heat capacitance model, as shownin FIG. 5, which illustrates a simplified section of a tank wall havingan imaginary characteristic volume defined by its mass (M) and specificheat capacity (C) and an adiabatic external boundary. The temperature ofthe characteristic volume can be the same as the temperature of the gas,for example, hydrogen.

This section of the tank wall, the characteristic volume, can have acombined mass and specific heat capacity, MC (kJ/K). Note that thecharacteristic volume and the associated MC are mathematicalconstructions only. Given knowledge of a tank design and the materialsused in the tank construction, it is possible to provide a reasonableestimation of the MC value. In the method disclosed herein, however,there is no need to calculate the exact mass and specific heat capacityof the tank because the characteristic volume simply acts as a heatsink, allowing its characteristics to be used in predicting the thermalbehavior of the tank system.

In applying the method the temperature of the characteristic volume isset to be equal to the temperature of the hydrogen in the tank at theend of the vehicle fill. This means that the characteristic volume hasboth high thermal conductivity and high convective heat transfercoefficient. In addition, Q_(Environment)=0, meaning that no heat istransferred out of the characteristic volume during the fueling(adiabatic boundary). As discussed supra, there is very little heattransfer to the environment during the refueling operation, allowingthis component of the heat transfer to be ignored. In an illustrativeexample, the heat transfer equation is solved for the target orpreferred end-of-fill condition of, for example, a fill time of 2 or 3minutes, plus some adjustment for longer fill times as deemed necessary.For the purposes of this disclosure, a target fill time of 3 minutes hasbeen used, but the method can be easily utilized for longer or shorterfill times.

When applying a characteristic volume in this manner, the heat that istransferred from the hydrogen mass, m_(cv) into the characteristicvolume can be described by the temperature rise during the fueling ofthe characteristic volume with a combined mass and specific heatcapacity of MC.

Q=MC(T _(final) −T _(initial))

-   -   where    -   MC=Combined Mass and Specific Heat Capacity of the        Characteristic Volume (kJ/K)    -   T_(final)=Temperature at the finish of the refueling (K)    -   T_(initial)=Temperature at the beginning of the refueling (K)

By applying an energy balance across the boundary of the control volume,and combining equation [5] (energy transferred from the hydrogen) withequation [7] (energy transferred to the characteristic volume) resultsin:

$\begin{matrix}{{Q = {m_{cv}( {u_{adiabatic} - u_{final}} )}}{{energy}\mspace{14mu} {transferred}\mspace{14mu} {from}\mspace{14mu} {the}\mspace{14mu} {hydrogen}\mspace{14mu} {control}\mspace{14mu} {volume}}} & \lbrack 5\rbrack \\{{Q = {{MC}( {T_{final} - T_{init}} )}}{{energy}\mspace{14mu} {transferred}\mspace{14mu} {to}\mspace{14mu} {the}\mspace{14mu} {characteristic}\mspace{14mu} {volume}}} & \lbrack 9\rbrack \\{{MC} = \frac{m_{cv}( {u_{adiabatic} - u_{final}} )}{( {T_{final} - T_{init}} )}} & \lbrack 10\rbrack\end{matrix}$

MC can then be determined directly from test data for a particularrefueling procedure by using Equation [10], which is the ratio of theheat transferred from the hydrogen to the temperature change of thecharacteristic volume. For Equations [9] and [10], T_(init)=T_(initial).The temperature, pressure and MC behavior associated with a 3-minutefill of a Type 3 tank is illustrated in FIG. 6. As reflected in thegraph, the MC is 62 at the end-of-fill point, but then increases overtime as the tank cools. This trend of MC over time can, in turn, be usedin predicting the result of longer filling procedures. Once an MC isknown for a given set of initial conditions, it can be used for directlycalculating the final temperature of refueling event.

Q=m _(cv)(u _(adiabatic) −u _(final))  [5]

Q=m _(cv) C _(v)(T _(adiabatic) −T _(final)), another identity ofequation 5  [11]

Q=MC(T _(final) −T _(init))  [9]

Combining equations [9] and [7] we get:

${T_{final} = \frac{{m_{cv}C_{v}T_{adiabatic}} + {MCT}_{init}}{{MC} + {m_{cv}C_{v}}}},$

combining equations [7] and [9]

-   -   where    -   C_(v)=specific heat capacity of hydrogen at constant volume,        kJ/(kgK)

Equation [12] can then be used to calculate the expected finaltemperature of a hydrogen tank refueling just as a fill has started. TheMC parameter and m_(cv) (the end-of-fill mass in the control volume) aretransmitted to the station. In a nonlimiting example, the MC parameterand m_(cv) are transmitted by RFID, through the SAE TIR J2799 IRDAinterface, or via an identification number that corresponds to entriesin a database that is readily accessible to the hydrogen tank fillingstation. The hydrogen tank filling station can calculate T_(adiabatic)from m_(cv) and parameters including 1) the initial pressure of the tankreceiving the hydrogen (e.g., the vehicle's tank), 2) the initialtemperature of the tank receiving the hydrogen (assuming ambientconditions plus some differences due to the possibility of a hot or coldtank as discussed in SAE TIR J2601) and 3) the enthalpy of the deliveredhydrogen, which is a function of the expected average temperature andpressure of the delivered hydrogen (further description is given in theAppendix provided in FIG. 24).

Certain characteristics of the MC Method make it particularly useful forgas delivery systems. For example, a particular dispenser, connector(s)and tank configuration can have a characteristic curve of MC v. filltime from which adjustments can be made to compensate for a range ofinitial conditions. Utilizing the MC model avoids the need to addressall of the intricacies of the temperature distribution within theconnecting components and the wall of the tank, especially over a timescale associated with typical hydrogen tank refueling procedures, e.g.,two to three minutes or more.

MC is not a direct physical constant such as the mass and the specificheat capacity of the connector component(s), tank and liner material butis, instead, a composite value, similar to an overall heat transfercoefficient, that encompasses heat transferred to or from tank valveassemblies and piping as well as heat transferred to the hydrogencomprising the initial gas volume inside the tank being filled. Systemswith slower heat transfer characteristics (convection or conduction)tend to result in lower values of MC (such as Type 4 tanks) whilesystems with faster heat transfer characteristics (convection orconduction) tend to result in higher values of MC (such as Type 3tanks). Although MC is a function of a number of different parametersincluding, for example, time, fill conditions, tank materials, tankconfiguration, etc., for a given tank, fill time and set of fillconditions, MC can be constant. The trend in the MC value over both timeand under different fill conditions can be predicted and, in turn,utilized for adjusting the hydrogen tank filling procedures to improveefficiency while maintaining desired safety margins.

Based on observations of several sets of test data coupled with the useof multiple linear regression for evaluating the significance of variousparameters, many possible physical models were considered for describingthe MC v. time curve and also describing the changes in initialconditions that were tested. In a non-limiting example, one model isrepresented by Equation [13], as shown below:

$\begin{matrix}{{{MC}( {U,t} )} = {C + {{Aln}( \sqrt{\frac{U_{adiabatic}}{U_{initial}}} )} + {g( {1 - ^{{- k}\; \Delta \; t}} )}^{j}}} & \lbrack 13\rbrack\end{matrix}$

or, in an alternative non-limiting example, Equation [13]′, as shownbelow:

$\begin{matrix}{{{MC}( {U,t} )} = {C + {A( \frac{U_{adiabatic}}{U_{initial}} )} + {g( {1 - ^{{- k}\; \Delta \; t}} )}^{j}}} & \lbrack 13\rbrack^{\prime}\end{matrix}$

-   -   where    -   C, A, g, k and j are constants derived from characterization        testing    -   U_(adiabatic) is the adiabatic internal        energy=m_(cv)u_(adiabatic)    -   U_(initial) is the initial energy=m_(initial)u_(initial)    -   Δt is the difference in time between the normally defined        end-of-fill time (e.g., 3 minutes) and the end-of-fill time that        achieves the desired final temperature.

In the context of Equation [13], C is a constant that represents aminimum heat capacity of, for example, a 2- or 3-minute fill, A is aconstant representing an adjustment to the MC corresponding to theinitial fill conditions and pre-cooling amount and constants g, k, and jare, if necessary, utilized within the MC Method to allow foradjustments to the resulting MC by extending the fill time beyond 2 or 3minutes, so that T_(final) can be optimized around a desiredtemperature. However, there are many possible models that can bedeveloped to predict the trend of MC with time, internal energy,pre-cooling temperature, etc. The improved MC Method is not intended to,and does not attempt to, perfectly describe the corresponding physicsbut is intended as an analytical engineering tool for predicting, withsufficient accuracy, the temperature outcome of a particular fillingprocedure by approximating the equivalent heat mass of the system.

One way to check a new model is to verify that the model is capable ofdescribing or predicting phenomena documented in previous literature.The Society of Automotive Engineers (SAE) conducted several sets ofhydrogen tank fill testing at Powertech during the development of SAETIR J2601, in support of, and to test the modeling efforts that werebeing conducted to build the refueling tables in SAE TIR J2601. By usingthe tables provided in SAE TIR J2601 as a set of test fills and plottingthe MC of each fill versus the fill time using Equation [10], theresults fall in a distinct pattern as illustrated in FIG. 7.

This result indicates that the equation utilized in the MC Method can beused to describe the MC v. Time over a wide range of conditions, and canbe used in place of the tables defined in SAE TIR J2601, which requireinterpolation between the listed data to find the appropriate pressureramp rate and end of fill pressure target. Because the MC Method canadjust the fill time to match a desired final tank temperature, it canbe used for any station configuration without relying on the rigid “TypeA, B, C, D” station type designations of SAE TIR J2601. Indeed, by usingthe coefficients of the MC v. time curve utilized in the improved MCMethod, a hydrogen tank filling station can directly calculate theexpected end-of-fill temperature (T_(final)) using Equation [12].

Using Equation [10], a series of fill tests were conducted with the MCv. time curve being plotted for each fill, as shown in FIG. 6. All ofthe tank fills follow a similar pattern of MC v. Fill Time as shown inFIG. 7. The resulting curve corresponds to the tank characteristic(s)for a given tank under a given set of conditions. To find thecoefficients used in Equation [13], the MC for each end-of-fill at 3minutes was plotted against the adiabatic internal energy divided by theinitial internal energy, as shown in FIG. 9A. The slope and intercept ofthe linear best fit line give the coefficient A and the constant Crespectively. The ΔMC v. Δtime, that is (MC_((t-180s))−MC_((180s))) v.(t−180 s), is then plotted as shown in FIG. 10, and a best fit modelused to determine the coefficients g, k and j. These coefficients canthen be used to describe how much heat is absorbed by the tank in thetime beyond the typical fill time and are particularly useful underconditions in which the ambient temperature is too warm and/or thepre-cooling temperature is too warm to achieve an end-of-filltemperature of less than 85° C. with a refueling time of 3 minutes orless.

To use the MC parameters for improving the performance of a hydrogentank filling station, a fueling protocol needed be developed. A fuelingprotocol should provide safe, high state of charge (SOC) fills, for abroad range of ambient conditions and initial fill conditions. Comparingthe current fueling standards with the actual operating ranges ofexisting hydrogen stations, as illustrated in FIG. 11, it is clear thatthe current refueling standards do not satisfy a broad range of stationfuel delivery operating conditions. Further, should a vehiclemanufacturer or modifier introduce a tank designed to operate at anotherpressure of, for example, 50 MPa, the fueling standard(s) would have tobe rewritten to accommodate this modification.

In order to fully utilize the improved MC Method at an actual fuelingstation, the relevant MC parameters must be communicated to ordetermined by the station in some manner. This data collection could beachieved in a number of ways. In a non-limiting example, one or more ofRFID, an IRDA interface as defined in SAE J2799 or other protocol suchas the proposed Hydrogen Vehicle Authorization System (HVAS) can be usedfor confirming that a vehicle is authorized to fuel (OEM vehicle or aconversion that meets safety requirements).

FIG. 12 shows both the vehicle side and station side information thatmay be used to fuel a vehicle based on the improved MC Method. Thestation can have access to both the vehicle side information throughvehicle communication and station side information through directmeasurement. The station then uses this parametric data in conjunctionwith the improved MC Method, for calculating an appropriate solution forfilling the particular vehicle.

In an embodiment, when applying the improved MC Method, the fuelingprocess can include two discrete steps. In the first step, parametricdata is used to determine an appropriate fueling fill rate, i.e., onethat does not overheat the gas in the tank. During the second step, thefueling fill rate is used to determine a target end-of-fill pressurethat can keep the system pressure within the target pressure ranges. Inorder to determine the appropriate fueling rate, the filling stationtakes into consideration both the capabilities of the vehicle's tanksystem and the station's capabilities for delivering fuel under thecurrent conditions.

Typical limits currently utilized in refueling operations, as defined inSAE TIR J2601 and TIR J2579 are 85° C. and 125% of the NWP for averagegas temperature and pressure, respectively. In an illustrative example,the station makes an assumption about the average gas temperature insidethe tank, based on measuring the ambient air temperature and optionallyadding a margin for a hot soak condition (e.g., the vehicle has beenparked in an environment that is hotter than ambient, such as a hotgarage or parking lot). The station also determines the approximateinitial SOC of the vehicle, using the temperature assumption and bydispensing a small amount of fuel to the tank to equilibrate the hosepressure to the tank pressure. Based on the tank pressure and vehicleside information, the station can estimate how much hydrogen (mass) mustbe delivered to the vehicle to achieve the desired SOC and, utilizing anestimate of its pre-cooling capability, the station can calculate theaverage enthalpy that can be delivered to the vehicle's tank systemduring the fill operation. Working from this information, the stationcan then determine how quickly to fill the vehicle while maintaining therequisite safety margin.

As explained supra, the primary MC parameter is based on a targetfueling time with additional parameters being used to account for theinitial SOC and/or fueling times that exceed the target fueling time.Starting with these targets, the station analyses an initial fillprotocol to determine if the fill can be successfully completed, i.e.,end-of-fill temperature within specification. If it is determined thatthe initial fill protocol cannot be successfully completed, an iterativeprocess is initiated to determine an appropriate fueling time. Forexample, if the fueling operation can be conducted in the target timewithout exceeding any temperature limits, the station can initiatefueling.

If, however, the initial fill protocol would cause a temperature limitto be exceeded, the projected fueling time can be increased by someincrement (e.g., 0.1, 1, 5, 10 seconds, etc.) and the new MC value canbe calculated. This iterative process can continue until an acceptablefueling time solution is identified. This process is shown in FIG. 13using a 10-second increment as an example. The output of this Step 1 isthe T_(final(Hot Soak Bound)) and the fueling or fill time. In anembodiment of the method, the appropriate fueling time can becontinuously or repeatedly calculated throughout the fill procedurebased on the actual enthalpy delivered to the vehicle. Accordingly, eventhough the fueling time calculated at the beginning of the fill shouldbe a good approximation, the fueling time (or rate of pressure riseduring the fill) can be adjusted as necessary to take into account theactual fill conditions if they vary across the fill cycle.

For the dispenser to make the assumption that the upper bound of gastemperature inside the tank is ambient T plus a ΔT hot soak, it mustknow that the vehicle has not been recently refueled. If thisinformation is unknown, then a more conservative assumption should beutilized, e.g., determining the fueling speed based on an empty ornearly empty tank. By using this more conservative assumption, even ifthe vehicle had been recently refueled, the calculated fueling speeddoes not overheat the tank.

If the recent fueling history of the vehicle can be determined, a lessconservative fueling speed can be utilized, potentially shortening thefueling time considerably. There are a number of approaches that can beutilized for determining the recent fueling history of the vehicle. Anon-limiting example is for the HVAS RFID tag to be time stamped eachtime the vehicle is fueled. The dispenser can then read this time stampeach time the vehicle is fueled and determine whether to use aconservative fueling speed if the time stamp indicates a recentrefueling, or a less conservative fueling speed based on the actualstarting pressure in the tank if the time stamp indicates refueling hasnot occurred recently.

Once the appropriate fueling time has been determined, the next step ofthe improved MC Method is to determine when, or at what pressure, tostop the fill operation. The process used by the station in this secondstep is similar to that used in the first step except that the stationassumes the gas temperature inside the tank at the beginning of the fillis below the ambient temperature, i.e., a cold soak condition, whichincludes the possibility that the tank has been soaked in an airconditioned garage, or that the ambient temperature is rising and theinternal gas temperature lags the ambient. There is also the factor ofdriving that may be considered in which the gas temperature inside thetank has been reduced as a result of the decrease in pressure as thehydrogen was consumed. The improved MC Method can be used to estimatethe average temperature of the MC and hydrogen gas during defuelingusing Equation [16]

$\begin{matrix}{{u_{adiabatic}(t)} = \frac{{U( {T_{ColdSoak},P_{NWP}} )} - {{m_{add}(t)}h_{exit}} + {Q_{connector}(t)}}{m_{initCold}}} & \lbrack 14\rbrack\end{matrix}$

-   -   where    -   m_(add)=mass exiting the hydrogen tank in time t    -   m_(add)=m_(cv)−m_(initCold)=mass to be added during the vehicle        refueling calculated in the MC Method to achieve 100% SOC    -   h_(exit)=average enthalpy of the hydrogen exiting the tank    -   Q_(connector)=the heat added by the connector components in time        t    -   m_(initCold)=mass in the tank just before refueling    -   t=time it would take to empty the tank from P_(NWP) to the        starting fill pressure P_(init)

$\begin{matrix}{t = \frac{m_{add}}{\overset{.}{m}}} & \lbrack 15\rbrack\end{matrix}$

-   -   where    -   {dot over (m)}=flow rate of hydrogen during defueling (g/s)    -   T_(ColdSoak)=assumed temperature of the vehicle tank before        defueling

T _(ColdSoak) =T _(ambient) −ΔT _(Cold)  [16]

And combined with Equation [13] where the T_(adiabatic) is determined bya curve fit to NIST data as before, then T_(final) is the averagetemperature of the MC and the gas in the tank.

$\begin{matrix}{T_{FinalDefuelCold} = \frac{{m_{cv}C_{v}T_{AdiabaticCold}} + {{{MC}(t)}T_{ColdSoak}}}{{MC} + {m_{cv}C_{v}}}} & \lbrack 17\rbrack\end{matrix}$

The appropriate ΔT_(Cold) parameter, and the defueling mass flow rate{dot over (m)}, can typically be determined by the OEM and can beprovided as part of the vehicle side information transferred throughHVAS or otherwise made available to the filling station.

Once the initial conditions have been determined, the station cancalculate how much mass must be added to the tank to reach the targetdensity of 100% SOC. If the station has an accurate flow meter, it cansimply integrate the mass flow during the fill and stop when the targetmass has been achieved, however, the application of a flowmeter in thiscapacity might have its own challenges. A second option is to calculatea pressure target utilizing the same set of equations as in Step 1.T_(final) can be calculated based on the fueling time of Step 1, andthen the P_(target) value can be calculated based on the pressure that,in conjunction with T_(final), provides a 100% SOC target density.

This process can be more easily understood by utilizing the equationsshown in FIG. 14. It is important to note that the pressure target canbe continuously calculated throughout the fill procedure based on theactual enthalpy delivered to the vehicle. Accordingly, even though thepressure target calculated at the beginning of the fill should be a verygood approximation, the pressure target utilized in stopping the fillcan be adjusted as necessary based on the actual fill conditions as theyoccur. The output of this Step 2 is the P_(Target).

In the case of a fill with communications, the initial temperature canbe measured directly by the station. Because this initial temperature isa settled temperature, i.e., a temperature not subject to the dynamicchanges associated with vehicle fueling, it is typically reliable. Insuch cases, the T_(init) is simply the measured initial temperature andthe hot soak and cold soak assumptions detailed above need not beconsidered.

During the fill testing conducted during development of the MC Method, a“Target T_(final)” value was calculated in order to evaluate any errorsbetween the expected result and the actual result. This “TargetT_(final)” is shown in FIGS. 16-18 and FIG. 20 to demonstrate theaccuracy of the MC Method. In a normal “ID-Fill,” Step 3 isunnecessary—the station does not need to calculate an expected result asthe fill protocol is fully defined by Step 1 and Step 2.

Using the fill rate from Step 1, and the Pressure Target from Step 2,the expected T_(final) can be calculated. Because the Pressure Targetcalculated in Step 2 is usually lower than the Pressure Target that wasassumed in Step 1, the resulting fill can tend to exhibit a slightlylower SOC % which, in turn, indicates that the gas density target needsto be reduced to match the Pressure Target at a higher T_(final) thanwas calculated in Step 2. Because a change in additional mass ofhydrogen added affects the T_(adiabatic), for greater precision it isnecessary to complete the outlined calculations in order to determinethe expected T_(final) and SOC % target.

The utility and flexibility of the MC Method provides many opportunitiesfor customization and refinement to encompass, for example, fuelingtimes of less than 3 minutes for tanks that start filling at high SOC.

To confirm the MC parameters calculated according to the proceduresdefined supra, and to confirm the accuracy of using these parameters inthe filling algorithm detailed supra, a fifth fueling test was conductedfor each of the previously tested tanks using conditions of ambienttemperature, initial fill amount, and pre-cooling temperature that weredifferent than the conditions used in characterizing the tank. Using thealgorithms discussed supra and illustrated in FIG. 13, the expectedfinal temperature T_(final) was calculated for fills conducted at 35MPa, 50 MPa and 70 MPa. For the Hot Soak (HS) margin of safety tooverheat, T_(HSinit)=Ambient Temp+7.5° C. was used, for the Cold Soak(CS) margin of safety to overfill, T_(CSinit)=Ambient Temp−10° C. wasused. For the target T_(final), T_(init)=Ambient Temp was used in thealgorithm illustrated in FIG. 15.

The results of a 35 MPa Type 3 Tank Confirmation Test are illustrated inFIG. 16. Although the original targets were set for delivering 0° C.gas, the hydrogen filling station being used for the evaluation wasactually delivering nearly 5° C. gas, which would be outside of the SAETIR J2601 tolerance of 0° C.±2.5° C. for a Type C station. Thisdemonstrates one of the practical challenges of defining a tighttolerance on the pre-cooling temperature—it is actually difficult toachieve and/or maintain, even in test conditions. In light of the notedcapabilities of the hydrogen filling station, the targets were adjustedfor using 4.8° C. as the temperature of the delivered gas, the 35 MPatank fill actual temperature measurement was within 1K of the calculatedT_(final). Further, although fill completion was targeted for 180seconds, the actual fill was finished in 196 seconds. As a practicalmeasure, in order to achieve an optimum fill time the Hot Soak Boundshould be set at 85° C., however, because the test was predicated on a3-minute fill target, the Hot Soak Bound is less than 85° C. The MCMethod algorithm can be further refined to improve performance for filltimes of less than 3 minutes.

The results of a 70 MPa Type 4 Tank Filled to 50 MPa Confirmation Testare illustrated in FIG. 17. In this instance, although the pre-coolerwas set for −20° C., it was determined that the pre-cooler was actuallydelivering −14.8° C. gas on average. This result once again reflects theactual difficulty of meeting SAE TIR J2601 tolerances of −20° C.+/−2.5°C. for a Type B station. In light of the observed performance, thetemperature targets were adjusted to reflect what −15° C. pre-coolingtargets would have been, given the same conditions otherwise. Althoughthis rendered the Hot Soak bound high at 89° C., this deviation is arelic of the pre-cooling temperature being out of specification.

Also noted were changes in temperature in the tank measured after theend-of-fill. These post-fill deviations represent a practical source oferror in temperature measurements in a hydrogen tank that may resultfrom, for example, thermocouple placement, temperature gradients withinthe tank and/or time lag. Given these errors, however, the actual fillresult was still remarkably close to the target, further validating themodel. Additionally, 85° C. was not utilized as a stop point in thesefills, thereby allowing the tanks to reach temperatures slightly above85° C. These minor temperature deviations were not consideredproblematic because transient temperatures above 85° C. are generallyknown and allowed pursuant to SAE J2579, the disclosure of which isincorporated by reference, in its entirety.

The results of a 70 MPa Type 4 Tank Confirmation Test are illustrated inFIG. 18. As reflected in the illustrated data, the 70 MPa tank testtemperature result was an essentially perfect match for the calculatedT_(final) Target.

Comparing the data obtained from the 4 test fills used to generate theconstants of Equation [11] to the data generated in the fifthverification fill and additional verification fills, the resultsreinforce the concept that the MC is characteristic for the tank and canbe used to predict the fueling result. This is demonstrated in thegraphs illustrated in FIGS. 19A and 19B in which the data generatedduring the Type 3 Tank confirmation tests detailed above is consistentwith the data used in determining appropriate values for the variousconstants utilized in Equation [11]. These results demonstrate that theMC Method is sufficiently robust to be applied confidently across arange of tank configurations and operating conditions.

Looking at the error from all of the fills conducted, as illustrated inFIG. 20, it is apparent that the MC Method yields very accurate resultsfor Type 3 and Type 4 tanks, typically falling within a range consistentwith that expected from variations in thermocouple placement and/or timelag errors. As shown in FIG. 20, the MC Method Model error is thedifference between T_(final) as calculated by the MC Method, and theactual final temperature result measured at the end of the fillprocedure. The actual pre-cooling temperature of the station was used asthe input to the enthalpy calculation rather than the pre-cooler setpoint, for the reasons described supra. Known or suspected sources oferror include, for example:

-   -   errors of the calculation in average enthalpy used,    -   calculation in mass of hydrogen delivered,    -   measurement of ambient temperature,    -   measurement of initial tank pressure,    -   measurement of final tank pressure,    -   measurement of final tank temperature (thermocouple placement,        lag, standard error)    -   calculation of the MC from the best-fit coefficients, and    -   difference between actual fill time and expected fill time (due        to station bank switching, flow differences, etc.),    -   heat transfer in or out of the hydrogen stream after the station        enthalpy measurement, and/or    -   differences in the actual tank temperature from the assumed        ambient temperature (hot spots, cold spots, etc.)

Given all of these possible sources of error, it is remarkable that thedata generated during testing suggests that a lumped heat capacity modelcan achieve a standard deviation of errors of 0.6K for Type 3 Tanks and2.4K for Type 4 Tanks. The “Definition Error” as shown in FIG. 20removes the error in calculating enthalpy, calculating mass, andcalculating MC coefficients by using the test data to determine theactual heat transfer, the actual average enthalpy of the fill, and theactual MC value, and using those to calculate T_(final). This removessubstantially all of the errors and approximations attributable to thecalculations of the MC Method itself, leaving only the measurementerrors as the source of error. This has a standard deviation of 0.3K forthe Type 3 tank and 1.3K for the Type 4 tank. The remaining portion ofthe errors is likely a result of measurement errors, thermocouple lagand/or differences between the assumed and actual conditions (such ascold spots in the tank after defueling). It was noted that as the paceof the testing increased the magnitude of the errors also tended toincrease, possibly as the result of differences between the assumed andactual conditions including, for example, residual cold spots remainingfrom the defueling operations conducted between filling tests.

A sensitivity analysis of the MC Method to variations in input errorswas conducted to examine the correspondence between known levels ofinput errors and the resulting output errors. As reflected in the datapresented in FIGS. 21A and 21B, respectively, the MC Method wasrelatively resistant to input errors with Type 3 tanks being moresensitive to variations in the initial temperature measurements whileType 4 tanks are more sensitive to variations in the temperaturemeasurement of the flow stream at the station. 10K errors in the initialtemperature measurement leads to 6K errors in T_(final) for both Type 3and Type 4 tanks. 10% errors in the hydrogen temperature measurement atthe station (used for the average enthalpy approximation) lead toT_(final) error of 6K for Type 3 tanks and 8K for Type 4 tanks. 10%errors in the calculated MC coefficients lead to errors of around 3K(and 3K represents approximately a 1% error in the density of hydrogen).These results demonstrate that the MC Method has significant robustnessto accurately describe vehicle fueling over a range of conditions andsuppress the effect of input errors.

As detailed above, utilizing the improved MC Method for refining FuelingProtocols can enhance a hydrogen station's fueling performance. Althoughan ID Fill fueling protocol was discussed supra, the improved MC Methodmay also be applied to conventional non-communication fuelingoperations, as well as full communication fueling operations, ascurrently defined in SAE TIR J2601. A comparison of fueling methods isshown in FIG. 22, which highlights the benefits that could be expectedto flow from incorporating the MC Method into all three types of fueling(i.e., ID Fill, Non-Communication and Full-Communication). Thesebenefits are further elaborated upon in the discussion provided infra.

In an ID Fill configuration, the fueling process is better adapted tothe tank that is being fueled, thus tending to provide reduced fuelingtime and increased SOC within the bounds of the uncertainties of theinitial conditions of the tank and the measurements at the station. Thefueling process is also better adapted to the station's real timecapabilities, thereby increasing operational flexibility and avoidingthe rigid, preset, tightly bounded temperature requirementscorresponding to the various station types as defined in SAE TIR J2601.The improved MC Method allows the filling process to self-adjust to thecurrent fueling capabilities of the station, thereby providing thepotential for simpler, more flexible and less costly hydrogen fillingstations. The flexibility of the improved MC Method allows a hydrogenfilling station to be “tuned” to the current operating environmentwhich, in turn, may allow for increased pre-cooling temperatures whilestill maintaining generally acceptable fueling times under mostconditions. The ability to run at higher pre-cooling temperatures canimprove station efficiency, lower costs and maintain customersatisfaction.

Fueling processes incorporating the improved MC Method as detailed supracould eliminate the need for the look-up tables currently utilized fornon-communication fueling in accord with SAE TIR J2601, resulting in thesame benefits as outlined above. The non-communication fuelingoperations could include calculations of the MC Parameters of theboundary condition tanks utilized in building the non-communicationlook-up tables. When operating at the Type A (−40° C.) or Type B (−20°C.) pre-cooling temperatures, the resulting range of fueling rates andpressure targets would be expected to be substantially the same, if notidentical, to those defined in the look-up tables.

The flexibility of the improved MC Method in addressing variations intemperature and pressure would reduce or eliminate the need for rigiddefinitions of Station Types as currently applied and would allow eachstation to operate more efficiently for its current environment, and todispense fuel at improved rates, regardless of its pre-coolingtemperature. Conversely, non-communication processes as defined in SAETIR J2601 must operate within very tight pre-cooling tolerances, and ifit falls outside them, cannot dispense fuel (resulting in unhappycustomers) until its margins are back within the specified range(s).

The improved MC Method fueling process can also be utilized with fullcommunication fueling, resulting in a number of benefits. SAE TIR J2601currently defines two types of communication fueling including 1) aDefault method in which fueling rates are the same as thenon-communication fueling rates defined in the look-up tables and 2) anAlt Method in which a more aggressive fueling rate can be utilized inthose instances in which a vehicle Temperature Signal can be utilized ina feedback loop to regulate the fueling rate in order to suppress oravoid an overheat condition. With the improved MC Method, the fuelingrate is determined at the beginning of the fill, just as describedabove, and is also checked during the fill based on the actual enthalpyof hydrogen delivered during the fill. With communications fueling, theinitial and transient conditions can be more tightly defined, givingeven better results. Incorporation of the improved MC Method would meanthat the Default and Alt Methods would no longer be needed—a singlecommunications fueling protocol could be defined and it would be adaptedfor the vehicle being fueled and the fueling conditions.

From a safety standpoint, the improved MC Method allows an additionalcross check on the Temperature Signal received from the vehicle. Becausethe station can calculate the expected temperature from the MCparameters and delivered enthalpy, it can cross reference this with thetemperature signal from the vehicle. The temperature signal at thebeginning of the fill procedure is generally constant so by using theactual measured initial temperature and the characteristic MCparameters, the vehicle fueling protocol can be fully defined, andhigher quality fill results can be achieved (as reflected in both SOCand fill time).

The improved MC Method Fueling Protocol can be utilized comprehensivelyby the station, for Identification Fueling, Non-Communication Fuelingand Full Communication Fueling, resulting in a fill protocol that isbetter adapted to the current capabilities of both the vehicle and thehydrogen filling station capabilities and takes into account the currentoperating environment to achieve higher quality fills.

An aspect of using the improved MC Method is the accurate prediction ofthe mass average enthalpy that can be delivered to the tank during arefueling procedure or event. As shown in FIGS. 21A and 21B, a 10K errorin the mass average temperature can result in a 6K to 8K error inT_(final), so it is important to accurately predict the enthalpy of theupcoming fill. In connection with the MC Method testing, a Runge-Kuttaapproximation was developed for average hydrogen enthalpy at the nozzlefrom stations using pre-cooling as illustrated below in Equation [12].

$\begin{matrix}{h = {\frac{1}{4}\begin{bmatrix}{( \frac{h( {T_{precooling},{( P_{StationInt} ) + {h( {T_{precooling},( {P_{StationInt} + \frac{P_{StationFinal} - P_{StationInt}}{4}} )} }}} }{2} ) +} \\{( \frac{h( {T_{precooling},{( {P_{StationInt} + \frac{P_{StationFinal} - P_{StationInt}}{4}} ) + {h( {T_{precooling},( {P_{StationInt} + {2\frac{P_{StationFinal} - P_{StationInt}}{4}}} )} }}} }{2} ) +} \\{( \frac{h( {T_{precooling},{( {P_{StationInt} + {2\frac{P_{StationFinal} - P_{StationInt}}{4}}} ) + {h( {T_{precooling},( {P_{StationInt} + {3\frac{P_{StationFinal} - P_{StationInt}}{4}}} )} }}} }{2} ) +} \\( \frac{h( {T_{precooling},{( {P_{StationInt} + {3\frac{P_{StationFinal} - P_{StationInt}}{4}}} ) + {h( {T_{precooling},( {P_{StationInt} + {4\frac{P_{StationFinal} - P_{StationInt}}{4}}} )} }}} }{2} )\end{bmatrix}}} & \lbrack 12\rbrack\end{matrix}$

-   -   Where    -   T_(precooling)=Expected Precooling Temperature    -   P_(StationInt)=P_(init)+ΔP_(StationInt)=Initial Hydrogen Tank        Pressure+Initial Station Pressure Drop    -   P_(StationFinal)=P_(Final)+ΔP_(StationFinal)=Final Hydrogen Tank        Pressure+Final Station Pressure Drop

During testing, it was found that ΔP_(StationInit)=5 MPa if the initialtank pressure was 2 MPa, 2 MPa if the initial tank pressure was 17 MPa,and 1 MPa at higher initial pressures. ΔP_(StationFinal) was assumed tobe 1 MPa in all cases. Therefore, the algorithm may be modified toreflect, more accurately, the conditions and performance of a particularstation. In an illustrative example, the station builder or operator maymodify the algorithm to more accurately reflect the conditions andperformance of the station.

During several test fills, deviations were noted between the pre-cooleroutput temperature and the actual temperature delivered at the nozzle.These deviations tended to follow a relationship with mass flow rate andpre-cooling level as illustrated in FIG. 23. In general, the higher flowrates and/or larger differences between the pre-cooling and ambienttemperatures can be reflected in greater temperature deviations betweenthe nozzle temperature and the pre-cooler set temperature. Therefore,such factors can be taken into account in the MC Method. In anon-limiting example, each station builder or operator may determinethis relationship(s) for the range of expected operating conditions andparameters in order to select an appropriate pre-cooling level that cantypically provide customer friendly refueling times. This flexibility isone of the benefits of the improved MC Method—it allows the station tocalculate the appropriate fill time for a particular pre-coolingtemperature based on the conditions of that fill and the capabilities ofthe tank itself.

The algorithms utilized in practicing the improved MC Method areprovided below. As the vehicle approaches the hydrogen filling station,the vehicle provides the station, via RFID, IRDA or other communicationmethod, parametric data for a further improved MC Method fill procedure.This parametric data can include, for example:

-   -   NWP    -   Tank Volume (or the station can calculate it with a pressure        pulse)    -   Hot Soak Assumption    -   Cold Soak Assumption    -   Constants of MC Equation    -   Other parameters as desired (Max Temp Allowed, Fastest Fill Rate        Allowed, Max ρ_(Target) Allowed, etc.)

Even if none of the parameters are communicated, the station can use theimproved MC Method to conduct the fill by utilizing default Constants ofthe MC Equation as derived from SAE TIR J2601, and the default Hot Soak,Cold Soak assumptions of SAE TIR J2601.

Step 1−Calculate the Fueling Time Using Hot Soak Assumption

T_(HSinit) = T_(ambient) + Δ T_(hot) Δ t = 0m_(init) = V × ρ_(initial)(T_(initial), P_(initial))m_(cv) = V × ρ_(target) m_(add) = m_(cv) − m_(initial)u_(initial) = u_(initial)(T_(initial), P_(initial))$h_{average} = \frac{\sum{m_{add}{h_{i}( {T,P} )}}}{m_{add}}$$u_{adiabatic} = \frac{{m_{initial}u_{initial}} + {m_{add}h_{average}} + Q_{connector}}{m_{cv}}$T_(adiabatic) = T(ρ_(target), P_(adiabatic), u_(adiabatic))${MC} = {C + {A\frac{U_{adiabatic}}{U_{init}}} + {g( {1 - ^{{- k}\; \Delta \; t}} )}^{j}}$$T_{Final} = \frac{{m_{cv}C_{v}T_{Adiabatic}} + {MCT}_{Initial}}{( {{MC} + {m_{cv}C_{v}}} )}$

-   -   If T_(final)>85 C (or other user specific limit), Δt=Δt+10 s.    -   Iterate from the top of Step 1.

As a practical measure, P_(adiabatic) can be assumed to be the MAWP withonly a very small error, since internal energy has a very weakrelationship with pressure.

Step 2—Calculate the Pressure Target Using Cold Soak Assumption

T_(CSinit) = T_(ambient) − Δ T_(cold)m_(init) = V × ρ_(initial)(T_(initial), P_(initial))m_(add) = m_(cv) − m_(initial)u_(initial) = u_(initial)(T_(initial), P_(initial))$h_{average} = \frac{\sum{m_{add}{h_{i}( {T,P} )}}}{m_{add}}$$u_{adiabatic} = \frac{{m_{initial}u_{initial}} + {m_{add}h_{average}} + Q_{connector}}{m_{cv}}$T_(adiabatic) = T(ρ_(target), P_(adiabatic), u_(adiabatic))${MC} = {C + {A\; \frac{U_{adiabatic}}{U_{init}}} + {g( {1 - ^{{- k}\; \Delta \; t}} )}^{j}}$$T_{Final} = \frac{{m_{cv}C_{v}T_{Adiabatic}} + {MCT}_{Initial}}{( {{MC} + {m_{cv}C_{v}}} )}$P_(Target) = P(ρ_(target), T_(Final))  and  ρ_(target) = 100%SOC${CPRR} = \frac{P_{Target} - P_{init}}{{180s} + {\Delta \; t}}$

Step 3 (if Necessary)—Calculate the Expected Result

T_(init) = T_(ambient)m_(init) = V × ρ_(initial)(T_(initial), P_(initial))m_(cv) = V × ρ_(target)$m_{add} = {{m_{cv} - {m_{initial}u_{initial}}} = {{{u_{initial}( {T_{initial},P_{initial}} )}h_{average}} = {{\frac{\sum{m_{add}{h_{i}( {T,P} )}}}{m_{add}}u_{adiabatic}} = {{\frac{{m_{initial}u_{initial}} + {m_{add}h_{average}} + Q_{connector}}{m_{cv}}T_{adiabatic}} = {{{T( {\rho_{target},P_{adiabatic},u_{adiabatic}} )}{MC}} = {{C + {A\; \frac{U_{adiabatic}}{U_{init}}} + {{g( {1 - ^{{- k}\; \Delta \; t}} )}^{j}T_{Final}}} = {{\frac{{m_{cv}C_{v}T_{Adiabatic}} + {MCT}_{Initial}}{( {{MC} + {m_{cv}C_{v}}} )}P_{Target}} = {P( {\rho_{target},T_{Final}} )}}}}}}}}$If  P_(Target) > P_(TargetColdSoak), ρ_(Target) = ρ_(Target) − 0.001  g/L.

-   -   Iterate From the Top of Step 3.

A hydrogen station can maintain a database of MC parameters that havebeen communicated to the station, and use the lowest performing MCparameter, tank volume, and lowest initial SOC % historically observed,to set the pre-cooling temperature for the system in order to achieve afast fueling rate given ambient temperature. In this way a station cankeep the pre-cooling temperature set at an economically optimal level.

Although the improved MC Method was developed and has been describedwith an emphasis on filling vehicle hydrogen tanks at hydrogen fillingstations, modification of the MC Method to improve its performance inconnection with fueling hydrogen busses or fueling systems withcryogenic gasses or liquids is certainly contemplated. Similarly, it isanticipated that the basic MC Method could readily be adapted for use inconjunction with compressed natural gas vehicle fueling, or fast fillingof vessels involving any industrial gas and/or for calculating theresulting temperature of any process in which a pressurized gas isinjected into a pressure vessel. The applicability of the improved MCMethod and the associated constants reflecting the thermodynamicproperties and behavior for other processes can be determined byapplying a similar test matrix as set out above in connection withcompressed hydrogen tank refueling for automobiles.

We claim:
 1. A method of filling a compressed gas tank comprising:calculating an initial hot soak temperature T_(HSinit) for an initialmass of gas within the tank; determining a projected fill time throughT_(HSinit) that is predicted to produce a gas final temperatureT_(final) no greater than a target temperature T; calculating an initialcold soak temperature T_(CSinit) for an initial mass of gas within thetank; determining a target pressure P_(target) through T_(CSinit) thatis predicted to produce a state of charge of 100% within the tank; anddelivering gas to the tank at a pressure ramp rate that achievesP_(target) at the projected fill time.
 2. The method of filling acompressed gas tank according to claim 1, wherein determining the filltime comprises: calculating a composite heat capacity value MC accordingto at least one of the equations“Mc(”U,t)=C+Aln(√(U↓adiabetic/ U↓minitial))+ g

(1−e ^(↑)(−k×t))

^(↑) jand“Mc(”U,t)=C+A(U↓adiabetic/ U↓minitial))+ g

(1−e ^(↑)(−k×t))

^(↑) j wherein C, A, g, k and j are constants specific to the tank,U_(initial) is the initial internal energy of the initial volume of gasand U_(adiabatic) is the adiabatic internal energy of a final mass ofgas after filling the tank and wherein U_(adiabatic) incorporates anadjustment for heat added by connection components, Q_(connector). 3.The method of filling a compressed gas tank according to claim 1,wherein determining the fill time comprises: calculating an initial massm_(init); calculating an additional mass m_(add) necessary to achievethe state of charge of 100% within the tank; calculating the initialinternal energy u_(initial); estimating the average enthalpy h_(average)to be delivered to the tank with the additional mass; calculating anadiabatic internal energy u_(adiabatic) and an adiabatic temperatureT_(adiabatic); calculating a composite heat capacity value MC accordingto the equation${MC} = {C + {A\frac{U_{adiabatic}}{U_{init}}} + {g( {1 - ^{{- k}\; \Delta \; t}} )}^{j}}$wherein C, A, g, k and j are constants specific to the tank.
 4. Themethod of filling a compressed gas tank according to claim 3,comprising: determining the values C, A, g, k and j for the tank.
 5. Themethod of filling a compressed gas tank according to claim 1, whereindetermining the target pressure P_(target) comprises: calculating acomposite heat capacity value MC according to the equation${MC} = {C + {A\frac{U_{adiabatic}}{U_{init}}} + {g( {1 - ^{{- k}\; \Delta \; t}} )}^{j}}$wherein C, A, g, k and j are constants specific to the tank, U_(initial)is the initial internal energy of the initial volume of gas andU_(adiabatic) is the adiabatic internal energy of a final mass of gasafter filling the tank to a state of charge of 100% and whereinU_(adiabatic) incorporates an adjustment for heat added by connectioncomponents, Q_(connector).
 6. The method of filling a compressed gastank according to claim 1, wherein determining the target pressureP_(target) comprises: calculating a cold initial mass m_(initC);calculating an additional mass m_(add) necessary to achieve the state ofcharge of 100% within the tank; calculating the initial internal energyu_(initial); estimating the average enthalpy h_(average) to be deliveredto the tank with the additional mass; calculating an adiabatic internalenergy u_(adiabatic), wherein u_(adiabatic) incorporates an adjustmentfor heat added by connection components, Q_(connector); calculating anadiabatic temperature T_(adiabatic); and calculating a composite heatcapacity value MC according to the equation${{MC} = {C + {A\frac{U_{adiabatic}}{U_{init}}} + {g( {1 - ^{{- k}\; \Delta \; t}} )}^{j}}};$wherein C, A, g, k and j are constants specific to the tank.
 7. Themethod of filling a compressed gas tank according to claim 4, whereindetermining the values C, A, g, k and j for the tank comprises:performing a plurality of test fills of the tank to a state of charge of100% at a target fill time, wherein the test fills encompass a pluralityof initial fill pressures and a plurality of pre-cooling temperatures;calculating an end-of-fill MC for each test fill according to theequation${{MC} = \frac{m_{2}( {u_{adiabatic} - u_{final}} )}{( {T_{final} - T_{initial}} )}};$plotting MC against U_(adiabatic)/U_(initial) and performing a best fitto determine the constant, C, and coefficient, A of the resulting curve.plotting ΔMC against Δt(time−target fill time) and performing a best fitmodel to the resulting curve to determine the coefficients g, k and jfor the equation:ΔMC=g(1−e ^(−kΔt))^(j).
 8. The method of filling a compressed gas tankaccording to claim 7, wherein: a first initial pressure is a state ofcharge of less than 10% within the tank; and a first pre-coolingtemperature is an ambient temperature.
 9. The method of filling acompressed gas tank according to claim 8, wherein: a second initialpressure is a state of charge of about 50% within the tank; and a secondpre-cooling temperature is less than 0° C.
 10. The method of filling acompressed gas tank according to claim 7, wherein: a first initialpressure is 2 MPa and a second initial pressure is a state of charge ofat least about 50% within the tank; and a first pre-cooling temperatureis an ambient temperature and a second pre-cooling temperature is −20°C.
 11. A method of refueling a hydrogen tank on a hydrogen poweredvehicle comprising: calculating a hot soak initial temperatureT_(HSinit) for an initial mass of gas within the tank; determining aprojected fill time through T_(HSinit) that is predicted to produce afinal hydrogen temperature T_(final) no greater than a targettemperature T; calculating a cold soak initial temperature T_(CSinit) aninitial mass of gas within the tank; determining a target pressureP_(target) through T_(CSinit) that is predicted to produce a state ofcharge of 100%; and delivering gas to the tank at a pressure ramp ratethat will achieve P_(target) at the projected fill time.
 12. A method ofoperating a hydrogen gas filling station comprising: obtaining a firstset of parametric data corresponding to a hydrogen powered vehicle;obtaining a second set of parametric data corresponding to stationcapabilities; obtaining a third set of parametric data corresponding toa refueling ambient; calculating a MC value based on the parametric dataobtained, wherein the parametric data incorporates an adjustment forheat added by connection components, Q_(connector); and determining aprojected fill time that is predicted to produce a gas final temperatureT_(final) no greater than a target temperature T and achieve a state ofcharge of 100% within the tank according to Equation [B] $\begin{matrix}{{T_{Final} = \frac{{m_{cv}C_{v}T_{Adiabatic}} + {MCT}_{Initial}}{( {{MC} + {m_{cv}C_{v}}} )}};} & \lbrack B\rbrack\end{matrix}$ and determining a target pressure P_(target) that ispredicted to produce a state of charge of 100% within the tank.
 13. Themethod of operating a hydrogen gas filling station according to claim12, wherein: the first set of parametric data is obtained directly fromthe hydrogen powered vehicle through a communication protocol selectedfrom a group consisting of RFID, HVAS and IRDA.
 14. The method ofoperating a hydrogen gas filling station according to claim 12, wherein:the first set of parametric data is obtained by identifying the hydrogenpowered vehicle and accessing a parametric database maintained outsidethe vehicle.
 15. The method of operating a hydrogen gas filling stationaccording to claim 12, wherein: the first set of parametric data isassigned default values and determining an adjusted final target densitysufficient to achieve the P_(target) at the T_(final).
 16. The method ofoperating a hydrogen gas filling station according to claim 12, wherein:the first set of parametric data includes at least one parameterselected from a group consisting of nominal working pressure, tankvolume, refueling history, time stamp of last refueling, trip odometervalue, initial hydrogen mass, initial gas temperature, maximum hot soaktemperature, maximum cold soak temperature, maximum defueling rate andmaximum fueling rate.
 17. The method of operating a hydrogen gas fillingstation according to claim 12, comprising: maintaining first and secondhydrogen fill assemblies, the first hydrogen fill assembly operating ata first pre-cooling temperature and the second hydrogen assemblyoperating at a second pre-cooling temperature, wherein the first andsecond pre-cooling temperatures are different; analyzing the first setof parametric data; and directing the hydrogen powered vehicle to thehydrogen fill assembly that provides a state of charge of 100%.
 18. Themethod of operating a hydrogen gas filling station according to claim12, comprising: calculating a target pre-cooling temperature sufficientto achieve a 3-minute fueling time through parametric informationselected from a data set consisting of vehicle fueling history, tankvolume, lowest historical initial state-of-charge percent, lowesthistorical tank MC value, and ambient temperature; setting andmaintaining a hydrogen fill assembly at the target pre-coolingtemperature for the duration of a vehicle refueling operation.
 19. Themethod of operating a hydrogen gas filling station according to claim12, comprising: predicting a defueled system temperature for a combinedsystem heat mass; setting T_(FinalDefuelCold), and initiating refuelingthrough T_(FinalDefuelCold).
 20. The method of operating a hydrogen gasfill station according to claim 12, comprising: obtaining a first subsetof the first set of parametric data, the first subset corresponding toparametric data associated with a first hydrogen tank onboard thehydrogen powered vehicle; obtaining a second subset of the first set ofparametric data, the second subset corresponding to parametric dataassociated with a second hydrogen tank onboard the hydrogen poweredvehicle; calculating T_(final1) through the first subset of parametricdata and T_(final2) through the second subset of parametric data;detecting the greater of T_(final1) and T_(final2) to determine a targetfueling speed; and detecting the lesser of T_(final1) and T_(final3) todetermine P_(target).
 21. The method of operating a hydrogen gas fillstation according to claim 12, comprising: initiating a hydrogen gasfill; adjusting the second set of parametric data during the hydrogengas fill to reflect measured station performance; adjusting the MC valueduring the hydrogen gas fill to reflect variations in the first set ofparametric data and measured fill performance data; calculating anadjusted fill time and P_(target) to reflect adjustments in the secondset of parametric data and MC value; and determining the adjusted filltime to control the fill speed and end of fill conditions.
 22. Themethod of operating a hydrogen gas fill station according to claim 17,wherein: the more efficient hydrogen fill assembly provides a benefitselected from a group consisting reduced fueling time, higherstate-of-charge percent, increased pre-cooling temperature, reducedenergy consumption and combinations thereof.